Simplify the following expression: $\dfrac{30n^2}{18n^2}$ You can assume $n \neq 0$.
$ \dfrac{30n^2}{18n^2} = \dfrac{30}{18} \cdot \dfrac{n^2}{n^2} $ To simplify $\frac{30}{18}$ , find the greatest common factor (GCD) of $30$ and $18$ $30 = 2 \cdot 3 \cdot 5$ $18 = 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(30, 18) = 2 \cdot 3 = 6 $ $ \dfrac{30}{18} \cdot \dfrac{n^2}{n^2} = \dfrac{6 \cdot 5}{6 \cdot 3} \cdot \dfrac{n^2}{n^2} $ $\phantom{ \dfrac{30}{18} \cdot \dfrac{2}{2}} = \dfrac{5}{3} \cdot \dfrac{n^2}{n^2} $ $ \dfrac{n^2}{n^2} = \dfrac{n \cdot n}{n \cdot n} = 1 $ $ \dfrac{5}{3} \cdot 1 = \dfrac{5}{3} $